Derivation of the Inverse Schulze-Hardy Rule

TL;DR

This paper provides the first theoretical derivation of the inverse Schulze-Hardy rule, explaining how the critical coagulation concentration inversely relates to coion valence in charged colloidal systems, complementing classical theories.

Contribution

It offers a novel theoretical derivation of the inverse Schulze-Hardy rule, expanding understanding of colloidal aggregation with multivalent coions.

Findings

Critical coagulation concentration inversely proportional to coion valence.

Theoretical foundation for the inverse Schulze-Hardy rule.

Complements classical Schulze-Hardy rule for counterions.

Abstract

The inverse Schulze-Hardy rule was recently proposed based on experimental observations (Cao et al., Langmuir, 2015, 31, 6610-6614). This rule describes an interesting new situation of the aggregation of charged colloidal particles in the presence of the multivalent coions. Specifically, it can be shown that the critical coagulation concentration is inversely proportional to the coion valence. Here the derivation of the inverse Schulze-Hardy rule based on purely theoretical grounds is presented for the first time. This derivation complements the classical Schulze-Hardy rule which describes the multivalent counterion systems.